Enumerative tropical algebraic geometry in R2

Details Enumerative tropical algebraic geometry in R2 Enumerative tropical algebraic geometry in R2

2003-12-31

arxiv.org/abs/math/0312530v4

Mathematics

Algebraic Geometry

83 pages, 20 figures, Version 4, to appear in the Journal of the AMS

Scientific paper

The paper establishes a formula for enumeration of curves of arbitrary genus in toric surfaces. It turns out that such curves can be counted by means of certain lattice paths in the Newton polygon. The formula was announced earlier in http://arxiv.org/abs/math.AG/0209253. The result is established with the help of the so-called tropical algebraic geometry. This geometry allows one to replace complex toric varieties with the Euclidean n-space and holomorphic curves with certain piecewise-linear graphs there.

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